In the below figure, $ A B $ and $ C D $ are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If $ O A=7 \mathrm{~cm} $, find the area of the shaded region.
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Given:

\( A B \) and \( C D \) are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle.

\( O A=7 \mathrm{~cm} \).

To do: 

We have to find the area of the shaded region.

Solution:

Radius of the larger circle $OA=R= 7\ cm$

Radius of the smaller circle $r =\frac{7}{2}\ cm$

Area of the shaded portion $=$ Area of the larger circle $-$ Area of the smaller circle

$=\pi R^{2}-\pi r^{2}$

$=\frac{22}{7}[(7)^{2}-(\frac{7}{2})^{2}]$

$=\frac{22}{7}[49-\frac{49}{4}]$

$=\frac{22}{7}[\frac{196-49}{4}]$

$=\frac{22}{7} \times \frac{147}{4}$

$=\frac{11 \times 21}{2}$

$=\frac{231}{2}$

$=115.5 \mathrm{~cm}^{2}$

The area of the shaded region is $115.5\ cm^2$.

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Updated on: 10-Oct-2022

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